Did OpenAI solve the wrong Navier-Stokes problem?(scientificamerican.com) |
Did OpenAI solve the wrong Navier-Stokes problem?(scientificamerican.com) |
SciAm writes "in a sense, the LLM found and exploited a loophole in the framing of the question". This is pure sensationalism. Choosing option (C) (out of an explicit list of four options) is neither a "loophole" nor something "found by the LLM"; everyone involved knew this was the option they were pursuing.
With the grumbling out the way, there is some actual scientific content to the article: there's a strong argument that OpenAI's method will not extend to the unforced case, leaving our understanding of NS incomplete. This negative result is itself new and interesting (and predicated entirely on the solution found by OpenAI)!
It seems to me that formulating problems at the boundary of human knowledge precisely is always going to be challenging and situations are bound to occur where you look back with the benefit of hindsight and wish that you had posed the question slightly differently based on some knowledge you didn’t have at the time.
> It did, however, unambiguously solve the problem according to the Clay Institute’s original formulation. The official problem statement, penned in 2000 by mathematician Charles Fefferman, offers an option called “C,” in which solutions are allowed to use an external force like OpenAI’s.
God, it’s embarrassing to read stuff like this. They’re making it seem as if everyone involved was either stupid or dishonest just so they can pretend they have a scoop here.
Maybe something interesting will fall over because of that, who knows?
For a counter-example the latter is easier since you can have a tricky external forcefield.
The forced version is easier since you can custom design the force function to get the result (it doesn't have to be a realistic force like stirring), so getting the blow-up might be regarded just as much a function of your bespoke force function as of the fluid dynamics itself, which is apparently what OpenAI did, pushing the definition of the force function being "smooth" to it's limit.
So, it appears OpenAI did legitimately meet the Millenium Prize solution criteria, but in the most unrealistic, and therefore least interesting, way possible.
The title is a bit misleading. The variant with a smooth forcing was one of the four valid variants in the Clay formulation. It is interesting to solve it. It is still an interesting and impressive result. The no force version is also interesting and remains unsolved. It isn’t reasonable to just dismiss the proof on the grounds that 26 years later we claim it was never that interesting. This is the first time I’ve seen this attitude.
Today, we are discussing if AI cheated by picking the easy problem to solve which means that we at least still comprehend what’s going on.
I wish mathematics and the rest of the human intellect wouldn’t turn into content marketing that is generated primarily to trigger strong human emotions.
I feel that this is going to hurt both AI and the disciplines that can benefit the most from it
I think you are agreeing with me? My point is that "the larger math community" failed to set the bounds of the problem correctly.
It reminds me of a junior coding bootcamp lecture I once gave many years ago before AI coding. One of the first slides said "Computers will do exactly what you say, not what you mean."
At the current rate (if they keep burning tokens on it, which maybe they won’t given the backlash) RH will be proven within a year and there will be some other thing that means it’s not actually that impressive…
Then why was it allowed as an option in the millennium prize statement?
What about Tristan Buckmaster and Levent Alpöge, did they also attempt to solve the same challenge? Didn’t they know it wasn’t interesting?
Surprisingly enough, being chosen by another actor as proxy for some group doesn’t actually resolve the problem that an individual may not always be an accurate proxy for the concerns of the group (and especially for the same descriptive aggregate group a generation after the proxy acts on their behalf.)
Yes, they were working on what is considered a niche case, the option C from the millennium statement for Navier-Stokes. The article explains that clearly, you can just read it and get the details
And yet another set of humans—Open AI marketers—made an error in how they sold the result of the preceding errors.
But its not news that computers are mere tools and that any error blamed on a computer involves at least two human errors, one of which is blaming the computer instead of the human(s) responsible.
Its perhaps a bit less obvious that every thing for which credit is given to a computer involves at least one human error—that of crediting the computer—and certainly can be more amusing when it involves a bunch of human errors.